The tree Constraint

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Abstract

This article presents an arc-consistency algorithm for the tree constraint, which enforces the partitioning of a digraph \(\mathcal{G}\) = ( \(\mathcal{V},\mathcal{E}\) ) into a set of vertex-disjoint anti-arborescences. It provides a necessary and sufficient condition for checking the tree constraint in \(\mathcal{O}(|\mathcal{V}| + |\mathcal{E}|)\) time, as well as a complete filtering algorithm taking \(\mathcal{O}(|\mathcal{V}| \cdot |\mathcal{E}|)\) time.